Finite Group DatabasebetaFinite Group Databasebeta| order | 12090 |
| isoclinism | isoclinic class of C5⋊(D13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×C5⋊(D13⋊C3) |
| unambiguous semidirect product | C5⋊(C31×D13⋊C3) |
| unambiguous semidirect product | (C13⋊C3)⋊(D5×C31) |
| unambiguous semidirect product | D65⋊(C3×C31) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C5⋊(D13⋊C3) |
| commutator, cosocle, hypocenter | C5×C13 | C2×C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C31 | C2×C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C31 | |
32 conjugacy classes of subgroups.
682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12090, 54);